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## Section: New Results

### On the Optimization of Recursive Relational Queries: Application to Graph Queries

Graph databases have received a lot of attention as they are particularly useful in many applications such as social networks, life sciences and the semantic web. Various languages have emerged to query graph databases, many of which embed forms of recursion which reveal essential for navigating in graphs. The relational model has benefited from a huge body of research in the last half century and that is why many graph databases rely on techniques of relational query engines. Since its introduction, the relational model has seen various attempts to extend it with recursion and it is now possible to use recursion in several SQL or Datalog based database systems. The optimization of recursive queries remains, however, a challenge. We propose $\mu$-RA, a variation of the Relational Algebra equipped with a fixpoint operator for expressing recursive relational queries. $\mu$-RA can notably express unions of conjunctive regular path queries. Leveraging the fact that this fixpoint operator makes recursive terms more amenable to algebraic transformations, we propose new rewrite rules. These rules make it possible to generate new query execution plans, that cannot be obtained with previous approaches. We have defined the syntax and semantics of $\mu$-RA, together with the rewriting rules that we specifically devised to tackle the optimization of recursive queries. We have also conducted practical experiments that show that the newly generated plans can provide significant performance improvements for evaluating recursive queries over graphs.

These results will be presented at the SIGMOD 2020 conference [9].